This company‘s mobile first aid kid hoists a modified Swiss flag, and it has another one on the back of the backpack:

And on the same page, they call it a “Swiss Army Knife of trauma first aid stations” and even show a picture of a real Swiss army knife. You know, with the Swiss coat of arms on it? If you’re just as confused as they are, this is the international first aid symbol:

This game by Canadian developer Hinterland Studio has a confusing approach to first aid signage, sometimes using the Red Cross logo and sometimes the Swiss flag. It’s even mixed in one and the same image:

In this clip you can also observe how the first aid thing on the wall has a Swiss flag on it.